English

On the Hasse-Arf property of local fields

Number Theory 2025-04-21 v1

Abstract

Let F/KF/K be a finite Galois totally & wildly ramified extension of complete discrete valuation fields. We say that the extension has the Hasse-Arf property if the ramification jumps in upper numbering are integers. We give necessary defining equations for FF in terms of the ramification jumps. In order for the Hasse-Arf property to hold, these equations become very strict. We prove that the last assertion is an equivalence condition, thus in terms of these defining equations, the Hasse-Arf property becomes an equivalence condition.

Keywords

Cite

@article{arxiv.2504.13606,
  title  = {On the Hasse-Arf property of local fields},
  author = {Ioannis Tsouknidas},
  journal= {arXiv preprint arXiv:2504.13606},
  year   = {2025}
}

Comments

15 pages. It is the analog of arXiv:2312.12753 for local fields. Compared to it, several assumptions have been removed and some examples added. It is a work in progress. Comments are welcome